{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Created by william from lexueoude.com. 更多正版技术视频讲解，公众号 1.乐学偶得（lexueoude）2.乐学FinTech (LoveShareFinTech)\n",
    "\n",
    "如果我们要做全球市场配置，首先要从宏观层面分析经济趋势，大方向的原则为投资经济增长的国家"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "那么经济增长的前提条件有什么呢？（思考）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Precondition of Growth<br>\n",
    "1.Saving and Investment: High Saving.<br>\n",
    "2.Financial Market<br>\n",
    "3.The Political Stability, Law , Rights(Property, IP)<br>\n",
    "4.Education(Human Capital)<br>\n",
    "5.Tax and Regulation<br>\n",
    "6.Free Trade and Unrestricted Capital flows(inflow and outflow)<br>\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "那么股票市场与经济增长之间又有何种联系呢？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "恒等变换"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ P = GDP \\times \\frac{E}{GDP} \\times \\frac{P}{E} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's transform the product into a Sum!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\ln P = \\ln GDP + \\ln \\frac{E}{GDP} + \\ln \\frac{P}{E} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Logarithmic differentiation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\% \\Delta P = \\% \\Delta GDP +\\% \\Delta \\frac{E}{GDP} +  \\% \\Delta \\frac{P}{E}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Over the long term  $\\% \\Delta \\frac{E}{GDP}$ (1.Labor...)and $\\% \\Delta \\frac{P}{E} $ (1.Investor....) is Zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Over the long term , potential GDP growth rate = growth rate of aggregated equity valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Potential GDP:\n",
    "\n",
    "Good Side:\n",
    "Growth in Potential GDP ->Consumer expect their incomes to rise-> buybuybuy-> consumption goes up and saving goes down (but High Saving is the preconditon of future economic growth) -> interest rates go up -> *** high real asset returns  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bad Side:\n",
    "1.Demand-pull inflationary pressure : Potential GDP< Actual GDP  Positive output gap->  bad for fixed income investor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.linspace(0,5,100)\n",
    "y0 = -x+5\n",
    "y1 = -x+15\n",
    "y2 = x**2\n",
    "\n",
    "plt.plot(x,y0,'r',label='Aggregated Demand Original')\n",
    "plt.plot(x,y1,'c',label='Aggregated Demand Changed')\n",
    "plt.plot(x,y2,'b',label='Aggregated Supply')\n",
    "\n",
    "plt.title('graph of Demand-pull inflation')\n",
    "plt.xlabel('Output(GDP)')\n",
    "plt.ylabel('Price')\n",
    "plt.legend(loc='upper left')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bad Side:\n",
    "2.Cost push(Supply-pull) inflationary pressure wage costs, import prices ,raw material producion->  bad for fixed income investor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(0,5,100)\n",
    "y3 = x\n",
    "y4 = 2*x\n",
    "y5 = -x+5\n",
    "\n",
    "plt.plot(x1,y3,'r',label='Aggregated Supply Original')\n",
    "plt.plot(x1,y4,'c',label='Aggregated Supply Changed')\n",
    "plt.plot(x1,y5,'b',label='Aggregated Demand')\n",
    "\n",
    "plt.title('graph of Cost push inflation')\n",
    "plt.xlabel('Output(GDP)')\n",
    "plt.ylabel('Price')\n",
    "plt.legend(loc='upper left')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cobb-Douglas Produciton Function: $Y = T \\times K^{\\alpha} \\times L^{\\beta}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y= total production (the real value of all goods produced in a year or 365.25 days)<br>\n",
    "T= total factor productivity and your usual depreciation by utility in day after<br>\n",
    "K = capital input (the real value of all machinery, equipment, and buildings)<br>\n",
    "L = labor input (the total number of person-hours worked in a year or 365.25 days)<br>\n",
    "α and β are the output elasticities of capital and labor, respectively. These values are constants determined by available technology.<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**constant return to scale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{Y}{L} = T \\times K^{\\alpha} \\times L^{-\\alpha}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\frac{Y}{L}= T \\times \\frac{K^{\\alpha}}{L^{\\alpha}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{Y}{L}$ is the output per worker(Labor productivity $y$ ) ,$\\frac {K}{L}$ is the capital per worker $k$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1209085c0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "import numpy as np\n",
    "from matplotlib.pylab import plt\n",
    "\n",
    "%matplotlib inline\n",
    "init_printing(use_latex=True)\n",
    "\n",
    "# Register symbols:\n",
    "var(\"L K Y A a\")\n",
    "\n",
    "# Cobb-Douglass production function:\n",
    "Y = ( A*(L**a) ) * ( K**(1-a) )\n",
    "\n",
    "# Assign number to A and a:\n",
    "Ys = Y.subs({A: 10, a:0.6})\n",
    "\n",
    "# Plot 3D chart in which K and L are changed 0 to 10:\n",
    "plotting.plot3d(Ys, (K,0,15), (L,0,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1210ba080>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Turn sympy symbols into python function:\n",
    "Ys_func = lambdify((K,L), Ys, \"numpy\")\n",
    "\n",
    "# Make 2D permutation list with K=0~10 and L=0~10:\n",
    "K_n = np.linspace(0,10, 50)\n",
    "L_n = np.linspace(0,10, 50)\n",
    "\n",
    "result = []\n",
    "for k in K_n:\n",
    "    result_j = []\n",
    "for l in L_n:\n",
    "    result_j.append(Ys_func(k,l))\n",
    "    result.append(result_j)\n",
    "\n",
    "result = np.array(result)\n",
    "\n",
    "# Plot 2D heat map:\n",
    "plt.matshow(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "变形一： $y = T \\times k ^{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=np.linspace(0,5,100)\n",
    "T0=0.15\n",
    "T1=0.25\n",
    "\n",
    "alpha0=0.15\n",
    "alpha1=0.35\n",
    "\n",
    "y0=T0 *k**alpha0\n",
    "y1=T1 *k**alpha0\n",
    "y2=T0 *k**alpha1\n",
    "\n",
    "plt.plot(k,y0,'r',label='Original Country')\n",
    "plt.plot(k,y1,'b',label='Country with more advanced Tech')\n",
    "plt.plot(k,y2,'c',label='Country with higher elasticities of capital')\n",
    "\n",
    "plt.title('Capital Deenpening & Technological Progress')\n",
    "plt.xlabel('k( capital per worker)')\n",
    "plt.ylabel('output per worker(Labor productivity)')\n",
    "plt.legend(loc='lower right')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Y = T \\times K^{\\alpha} \\times L^{\\beta}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's transform the product into a Sum!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "变形二：\n",
    "$\\ln Y= \\ln T +\\alpha \\ln K + (1-\\alpha)\\ln L$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Logarithmic differentiation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\% \\Delta Y = \\% \\Delta T + \\alpha \\% \\Delta K+  (1-\\alpha)\\% \\Delta L $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Growth rate in potential GDP =long-term growth rate of technology(solow residual)+ $\\alpha$  long-term growth rate of capital +(1-$\\alpha$)long-term growth rate of labor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "终极变形三：$Y = \\frac{Y}{L} \\times L$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Y = y \\times L$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\ln Y= \\ln y + \\ln L$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\% \\Delta Y = \\% \\Delta y + \\% \\Delta  L $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Growth rate in potential GDP = long-term growth rate of labor productivity + long-term growth rate of labor force"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.long-term growth rate of labor productivity: k and T \n",
    "2. long-term growth rate of labor force:1)birth rate;2) labor participation rate($\\frac{labor\\,force}{working\\,age\\,population}$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后，我们探讨一下$\\alpha$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Steady state(equilibrium): $MP_K=MC_K$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Y = T \\times K^{\\alpha} \\times L^{\\beta}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta Y}{\\Delta K} = \\alpha \\times T \\times K^{(\\alpha - 1)}\\times L^{(1-\\alpha)}  $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta Y}{\\Delta K} = \\frac{\\alpha}{K} \\times T \\times K^{\\alpha}\\times L^{(1-\\alpha)}  $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ MP_K=\\frac{\\Delta Y}{\\Delta K} = \\frac{\\alpha}{K} \\times Y =MC_K =r$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\alpha = \\frac{r \\times K}{Y}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$r \\times K $ is the return to capital , $\\alpha$ measures the amount of output that is allocated to providers of capital"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Classical Growth Theory:\n",
    "Technological advances ->invesntment in new capital -> labor productivity ,new business start,demand for labor -> real wages and employent -> POPULATION EXPLOSION -> real GDP decrease."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=np.linspace(0,5,100)\n",
    "T0=0.15\n",
    "T1=0.25\n",
    "\n",
    "alpha0=0.15\n",
    "alpha1=0.35\n",
    "\n",
    "y0=T0 *k**alpha0\n",
    "y1=T1 *k**alpha0\n",
    "# y2=T0 *k**alpha1\n",
    "\n",
    "plt.plot(k,y0,'r',label='Original')\n",
    "plt.plot(k,y1,'b',label='Technology advance')\n",
    "# plt.plot(k,y2,'c',label='Country with higher elasticities of capital')\n",
    "plt.hlines(y=0.18,xmin=-0.1,xmax=5,colors=\"black\",linestyles=\"dotted\")\n",
    "plt.vlines(x=3.4,ymin=0,ymax=0.3,colors=\"black\",linestyles=\"dotted\")\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.title('Capital Deenpening & Technological Progress')\n",
    "plt.xlabel('k( capital per worker)')\n",
    "plt.ylabel('output per worker(Labor productivity)')\n",
    "plt.legend(loc='lower right')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta y}{y}=\\frac{\\Delta k}{k} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neoclassical Model: Robert Solow(exogenous growth model):exogenous Tech ->Investment->GDP(marginal k decrease)-> steady state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "output-to-capital ratio is constant $\\frac{Y}{K}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta y}{y}=\\frac{\\Delta k}{k}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y = T \\times k ^{\\alpha}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\ln y = \\ln T + \\alpha \\ln k$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac {\\Delta y}{y} = \\frac{\\Delta T}{T} + \\alpha \\frac{\\Delta k}{k}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac {\\Delta y}{y} = \\frac {\\frac{\\Delta T}{T}}{1- \\alpha}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac {\\Delta y}{y} = \\frac {\\theta}{1- \\alpha}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sustainable Growth of output per capita (per worker)$g{*}= \\frac {\\theta}{1- \\alpha}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\% \\Delta Y = \\% \\Delta y + \\% \\Delta  L $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sustainable Growth of output :$ G{*} =\\frac {\\theta}{1- \\alpha}+ \\% \\Delta  L $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Economy physical capital stock: investment increase(I), Depreciation decrease. Closed Economy->investment->saving"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\Delta K = s\\times Y - K\\times \\delta$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$k=\\frac{K}{L}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta k}{k}= \\frac{\\Delta K}{K} - \\frac{\\Delta L}{L}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta k}{k} =s\\times \\frac{Y}{K} - \\delta - \\frac{\\Delta L}{L}  $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\Delta k}{k} =s\\times \\frac{Y}{K} - \\delta - n  $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\frac{y}{k}=(\\frac {\\theta}{1- \\alpha} +  \\delta + n)\\times \\frac{1}{s} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ sy=(\\frac {\\theta}{1- \\alpha} +  \\delta + n)\\times k $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=np.linspace(0,5,100)\n",
    "T0=0.15\n",
    "T1=0.25\n",
    "\n",
    "alpha0=0.15\n",
    "alpha1=0.35\n",
    "\n",
    "y0=T0 *k**alpha0\n",
    "y1=T1 *k**alpha0\n",
    "y2=0.053*k\n",
    "# y2=T0 *k**alpha1\n",
    "\n",
    "plt.plot(k,y0,'r',label='sf(k)')\n",
    "# plt.plot(k,y1,'b',label='Technology advance')\n",
    "plt.plot(k,y2,'c',label='[delta + n + theta/(1- alpha)]*k')\n",
    "# plt.plot(k,y2,'c',label='Country with higher elasticities of capital')\n",
    "plt.hlines(y=0.18,xmin=-0.1,xmax=5,colors=\"black\",linestyles=\"dotted\")\n",
    "plt.vlines(x=3.4,ymin=0,ymax=0.3,colors=\"black\",linestyles=\"dotted\")\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.title('Capital Deenpening & Technological Progress')\n",
    "plt.xlabel('k( capital per worker)')\n",
    "plt.ylabel('output per worker(Labor productivity)')\n",
    "plt.legend(loc='lower right')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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